Stats 2
Essay by 24 • April 8, 2011 • 1,127 Words (5 Pages) • 1,035 Views
ADM 2304 E - Statistical Methods Assignment #1
Problem 1
a)
Test and CI for Two Proportions: bmi_A, bmi_B
Null Hypothesis: No significant difference
Alternative Hypothesis: Significant difference
Event = 1
Variable X N Sample p
bmi_A 192 1342 0.143070
bmi_B 97 720 0.134722
Difference = p (bmi_A) - p (bmi_B)
Estimate for difference = 0.143070 Ð'- 0.134722 => 0.00834782
90% CI for difference = (-0.0178288, 0.0345244)
Test for difference = 0 (vs not = 0) Z = 0.52 P-Value = 0.600
Therefore, based on these results we would not reject the null hypothesis. There is no significant difference in the weights of both cities.
Manual
Pooled P-hat = (192 + 97) / (1342 + 720)
= 289 / 2062
= 0.140155
Z-stat = (0.143070 Ð'- 0.134722) Ð'- 0 / sqrt[(0.140155) x (1-0.140155) x (1/1342) x(1/720)]
= 0.008348 / 0.016037
= 0.520546
b)
Confidence Interval = (p1 Ð'- p2) +/- ZÐ"ÐŽ/2 * [sqrt ((p1(1-p1)/n1) + p2(1-p2)/n2)]
= (0.143070 Ð'- 0.134722) +/- 1.645 * [sqrt(0.14307(1-0.14307)/1342) + 0.134722(1-0.134722)/720)
= 0.008348 +/- 0.026179
Therefore this equals the interval of
(-0.0178288, 0.0345244)
The confidence interval calculated above is consistent with the conclusion in question A.
Problem 2
a)
Test and CI for One Proportion: C3
Test of p = 0.5 vs p not = 0.5
Event = 1
Variable X N Sample p 95% CI Exact P-Value
C3 1247 1937 0.643779 (0.621990, 0.665132) 0.000
b & c)
Test and CI for One Proportion: C4, C5, C6, C7, C8, C9, C10, C11, ...
Test of p = 0.5 vs p not = 0.5
Event = 1
Variable X
C4
C5
C6
C7
C8
C9
C10
C11
C12
C13
C14
C15
C16
C17
C18
C19
C20
C21
C22
C23 N
8
16
13
17
10
13
12
14
14
13
15
16
12
16
15
18
18
14
15
14 Sample p
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23 90% CI
(0.184473, 0.511179)
(0.537839, 0.853466)
(0.395195, 0.735240)
(0.588527, 0.889734)
(0.264760, 0.604805)
(0.395195, 0.735240)
(0.441309, 0.776082)
(0.350413, 0.693065)
(0.441309, 0.776082)
(0.395195, 0.735240)
(0.488821, 0.815527)
(0.537839, 0.853466)
(0.350413, 0.693065)
(0.537839, 0.853466)
(0.488821, 0.815527)
(0.641141, 0.924076)
(0.641141, 0.924076)
(0.441309, 0.776082)
(0.488821,
...
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